The source said New England had offered a five-year deal to the 27-year-old Talib, but he opted not to take it because the market for free agent cornerbacks has been so soft this year.

There were offers from three other teams, including, according to one report, Washington, where Talib’s former head coach in Tampa Bay, Raheem Morris, is the defensive backs coach.

Talib chose to stay in New England.

Ultimately, the deal could be a win-win for both sides. Though he was a good soldier in his first two months as a Patriot, Talib has a history of off-field issues and also has dealt with his share of injuries. If either of those things becomes a problem, New England can move on without a great financial loss.

And for Talib, if he keeps his nose clean and plays well, he will hit the market again in 2014 with the chance to see if he can get a big payday.

New England chose to release Lloyd rather than pay him a $3 million option bonus that had to be exercised by 4 p.m. Saturday.

The Patriots specifically built some protection into the three-year contract Lloyd signed last year because he had the reputation for being hard to handle in his many previous stops. The Patriots were his sixth team in nine years.

The move to release Lloyd will clear $4.9 million off the Patriots’ cap, but there is $2 million in dead money. Under league rules, it could be split over two years if he is designated as a post-June 1 cut.

Lloyd was productive for the Patriots last season with 74 catches for 911 yards and four touchdowns, but he was very inconsistent on the field as far as staying on his feet, fighting for the ball, and developing a rapport with quarterback Tom Brady.

He also was a handful in the locker room and on the practice field with his at-times difficult personality. His erratic behavior included days of being moody or surly, and if he didn’t want to engage in a conversation, he would simply walk away, whether it was from a teammate or a reporter.

Lloyd played for Patriots offensive coordinator Josh McDaniels both in Denver when McDaniels was head coach there and in St. Louis in 2011, when McDaniels was in charge of the Rams’ offense. The receiver-needy Rams traded for Lloyd midway through the 2011 season.

As he approached free agency last year, Lloyd made it known: He wanted to go wherever McDaniels ended up, and thus he signed with the Patriots.

Since the Patriots, as of Saturday night, no longer had a receiver on the roster who caught a pass for them in 2012, Lloyd could be back, but at a lower cost if there’s not another team willing to sign him.

Talib most certainly will be back, at least for 2013, and keeping him means the Patriots will have a measure of depth at cornerback that they haven’t had in some time — provided Alfonzo Dennard will be with the team at the start of the season (he will be sentenced April 11 following a conviction for felony assault on a police officer), and with Kyle Arrington in the slot position, New England will be able to play to the strength of each player.

If Ras-I Dowling is finally healthy enough to stay on the field, it strengthens the position further.

Acquired from the Buccaneers at last season’s NFL trading deadline, which was Nov. 1, Talib played in eight games, including the postseason, and had an interception return for a touchdown in his first game in a Patriots uniform.

But a hip injury popped up against Houston in Week 14 against the Texans; though he played the next game against San Francisco, Talib played just eight snaps against the Jaguars and sat out the regular-season finale against Miami.

He was on the field for all but one snap in the divisional playoff game against Houston, but was forced out of the AFC title game against Baltimore early and New England could not adjust.

This has not been a good year financially for free agent cornerbacks. Once players started signing, they were getting deals worth far less than cornerbacks received in 2012.

The first to sign was Dominique Rodgers-Cromartie, who went to Denver on a one-year deal worth a reported $5 million.

Then the Chargers signed former Jaguar Derek Cox for a reported four years, $20 million, with $10.25 million guaranteed. On Thursday, the Chiefs added former Dolphin Sean Smith. Smith, who had been courted by a few teams, received three years, $18 million, with $11 million guaranteed from Kansas City.

Contrast that with last year: Lardarius Webb received six years, $52.74 million, with $10 million guaranteed, to remain in Baltimore; Tampa Bay got Eric Wright away from Detroit with a five-year, $37.5 million contract that guaranteed $15.5 million, and Brandon Carr became a Cowboy when he was given five years, $50.1 million, and half of it guaranteed.

So the market was definitely on the Patriots’ side, and they also saved in another way: Had New England franchised Talib this year, the cost would have been $10.85 million — more than twice what the Patriots will end up paying him for 2013.

. . .

Linebacker Niko Koutouvides re-signed with the Patriots on a one-year deal, according to the NFL Network.

Greg A. Bedard of the Globe staff contributed to this report. Shalise Manza Young can be reached at syoung@globe.com. Follow her on Twitter @shalisemyoung.